Smooth trajectory

Creates a smooth, periodic trajectory.

Collaboration diagram for Smooth trajectory:

The trajectory is made as

\( y_n(t) = b_n + a_n * \sin^3(2*pi*(t-t_{0,n})/T_n + p_n), t>t_{0,n}\, \text{and}\, t < t_{stop,n}\), where

• \(t\) is current time
• \(t_{0,n}\) is the start time for signal \(n\)
• \(t_{stop,n}\) is the stop time for signal \(n\)
• \(a_n\) is the amplitude for signal \(n\)
• \(p_n\) is the phase (in radians) for signal \(n\)
• \(b_n\) is the bias for signal \(n\)
• \(T_n\) is the period for signal \(n\)

Author

Karl-Johan Reite

Date

27.08.2013 KJR: Initial version.

Example configuration excerpt

<Lib
  LibName   = "fhsim_base"
  SimObject = "Src/SmoothTrajectory"
  Name      = "trajectory"
  Start     = "0,2"
  Stop      = "10,12"
  Amplitude = "2,4"
  Bias      = "1, 0"
  Phase     = "0, 3.14"
  Period    = "10, 1"
  PortWidth = "2"/>

Configuration parameters

Name	Width	Description
Start	<PortWidth>	The start time.
Stop	<PortWidth>	The stop time.
Phase	<PortWidth>	The phase (in radians).
Period	<PortWidth>	The period (in seconds).
Amplitude	<PortWidth>	The amplitude of the signal.
Bias	<PortWidth>	The signal bias.
PortWidth	1	The signal portwidt.

Output Ports

Name	Width	Description
Out	1	The output signal.

Initial conditions

This SimObject contains no initial conditions.

Full example file

<Contents>
  <OBJECTS>
    <Lib
        LibName="base"
        SimObject="Src/SmoothTrajectory"
        Name="A"
        Period="6.28318530718"
        Phase ="0"
        Stop="100"
        Start="0"
        Amplitude="1"
        Bias="0"
    />
  </OBJECTS>
 
  <INTERCONNECTIONS>
    <Connection
    />
  </INTERCONNECTIONS>
 
  <INITIALIZATION>
    <InitialCondition
    />
  </INITIALIZATION>
 
  <INTEGRATION>
    <Engine
    IntegratorMethod="2"
    NumCores="1"
    TOutput="0, 0:0.5:10, 30"
    LogStates ="1"
    stepsize ="0"
    HMax="0.002"
    HMin="0.00000001"
    AbsTol="1e-3" RelTol="1e-3"
    UseRSSNormInsteadOfInfNorm="0"
    FileOutput="objects:all"
    />
  </INTEGRATION>
</Contents>

This SimObject is referred to as Src/SmoothTrajectory